Rational escalation of costs by playing a sequence of unfavorable gambles: the martingale

Playing the martingale strategy is an anomaly, reverse to that observed in the St. Petersburg paradox. This paper rationalizes the demonstrated irrationality of playing, by characterizing necessary and sufficient conditions under which a utility maximizing decision maker would play the strategy. An individual willing to play the martingale may not be deterred by a finite cap on wagers. Individuals will continue with the strategy in the face of mounting consecutive losses which is, thus, sequentially rational. These results give insight into instances of escalating commitment to a losing cause, by analyzing one specific instance of such behavior.

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